i need your advise…..Iâ€™m having the exact the same problems with your water for couple of weeks now. Both of my Bradford white gas heaters are 6 years old and it happened just right after my warranty expired. Both water heaters will stay lit until it reaches setting temperature then everything shuts off. And if both set at warm or cooler it will stay lit. i have replaced thermostat, thermocouple, relieft value and reset switch for both heaters. I had the gas company to come to checked the gas pressure and pressures are good. I can understand if one of my heater is bad, but not both having the same problems.
Did you find out what causes your water to shut it off when it reaches the temperature setting?